In this work we are interested in embedded pairs for the optimal strong stability preserving (SSP) explicit Runge–Kutta methods. SSP explicit RK methods are extensively used in numerical computation of hyperbolic conservation
with total variable diminishing (TVD) spatial discretization [1]}, [2]}, [3]}, [4]}.
In many hyperbolic PDE applications, the step-size is controlled by monitoring the CFL number, defined by
\(\nu & = \frac{c_\text{max} \Delta t}{\Delta x}\) 
